The members of Greta Van Fleet were working on their debut album last month at a Nashville recording studio when actor Tom Hanks swung by and offered his nod of approval.

Hanks had been down the hall, where his wife, Rita Wilson, was recording, and the two-time Oscar winner — whom the young members of Greta Van Fleet recognize as the voice of wholesome cowboy Woody from Pixar’s “Toy Story” films — got a taste of their sound and expressed his fanfare for the group.

Hanks isn’t the only one on board with Frankenmuth’s throwback rock quartet. Earlier this year, Greta Van Fleet played Elton John’s Oscar party, at the request of Sir Elton himself. Bob Seger let the group open for him in concert last year. And Justin Bieber pulled up in his Lamborghini to a recent show in Los Angeles, after catching their set at Coachella.

Now the band is prepping for a slew of live dates — including three sold-out concerts next week at the Fillmore Detroit and slots at Austin City Limits and Chicago’s Lollapalooza festivals — all before their debut album is completed, let alone released.

It sure beats the other career options in Frankenmuth.

“The alternative was working at Bronner’s,” Jake says.

Even without Bronner’s, in a way, it’s still Christmas every day for Greta Van Fleet. The band has garnered a bigger buzz than any other rock band in years by cultivating a howling sound that borrows from — some would say borrows a little too liberally from — ’70s rock icons Led Zeppelin.

Go ahead and compare them to Zeppelin, says Greta bassist Sam Kiszka.

“I think that Led Zeppelin is the greatest rock ‘n’ roll band of all-time,” says Sam, on the phone from Nashville, taking a break from last-minute album tweaks on a recent afternoon. “There’s not many competitors to that sound. So when someone says, ‘You sound just like Led Zeppelin!’ I say, ‘thank you very much.’ ”

He understands the comparisons, but says the group’s debut album, tentatively due out in July, will paint a more complete picture of Greta Van Fleet.

“This record is going to be a heavy hitter,” Sam says of the as-yet-untitled set, which was mostly recorded live and is produced by Kid Rock affiliates Al Sutton and Marlon Young. “We poured our hearts and souls into this thing. I think it’s the start of something very serious.”

The album follows the group’s two 2017 EPs, “Black Smoke Rising” and “From the Fires.”

“We’re sort of looking at this as an evolution of the first two EPs,” says Jake. “We’ve been nurturing a lot of material, and I think a lot of the chaos that’s been going on around us, and the ruthless touring, has come off on the album.”

After growing up playing music around the house, brothers Jake, Sam and Josh Kiszka formed Greta Van Fleet (with drummer Kyle Hauck) in 2012. Their first show was at Frankenmuth’s annual Auto Fest, and they loaded their gear onto the back of a wooden trailer and played a set of cover songs.

“We cycled through all the songs that we knew, and then we were like, what do we do now?” says Sam. “My mom goes, ‘Play ’em again!”

They played ’em again, and again and again in bars and clubs in which they were too young to drink and eventually on bigger and bigger stages. They swapped out drummers — Danny Wagner replaced Hauck in 2013 — and graduated from cover songs to originals.

Eventually, the band earned a steady following that reaches far beyond the confines of Frankenmuth, the small town 100 miles north of Detroit that was best known for its fried chicken before Greta came along.

Their fan base stretches from kids to adults, in part because their sound is so out of step with today’s pop music.

“We don’t really fit into the current music scene,” says Sam, who at 19 is three years younger than his twin older brothers. “But I think it’s about time for a change. I think people are tired of what’s on pop radio, and I think they’re tired of being lied to.”

The timelessness of rock ‘n’ roll is what drew them to it, says Jake, and it’s why they’re putting their own spin on it and passing it on. “It’s familiar to generations who grew up listening to it, and it’s familiar to our generation having listened to it,” he says. “We’ve all been influenced by (rock ‘n’ roll), and we’re carrying that forward.”

The band’s energy, look and enthusiasm has all been big contributors to its boom in popularity, says Mark Pennington, program director at WRIF-FM (101.1).

“It’s amazing how this band has taken off,” says Pennington, who sees long-term success in the band’s future. WRIF had Greta Van Fleet on the bill as part of last summer’s Riff Fest at DTE Energy Music Theatre, and on a bill that included Rob Zombie, Five Finger Death Punch, Pop Evil and more, Greta was the most-talked about band, he says.

On a local level, Pennington says he hasn’t seen a local act break big in this way since Kid Rock.

“They caught lightning,” Pennington says, “and they’re riding it.”

While Frankenmuth has shown its support — a portrait of the band hangs in the halls of Frankenmuth High School, Jake says — the band considers its upcoming run of Detroit shows as a hometown stand.

“Anytime we play Michigan it really feels like we’ve come home. The reception’s always there, and there’s always people waiting for us,” Jake says. “When we come home, it feels like we’re back, and we like to showcase what we’ve learned all along the way.”

After the Detroit concerts, the circus continues — Europe, South America and Asia are all on the docket for the rock ‘n’ rollers, which they’ll handle by taking everything as it comes.

“When you’re dealing with so much at such an extensive pace, there’s an element to taking things day-to-day and not necessarily knowing what’s going on one week from now, or two weeks from now,” Jake says. “We like to keep ourselves in a constant state of confusion, so we never know what’s actually going on.”